Question

annette is surveying people in the city about their interest in a new shopping mall. she found that 180 people, or 37.5% of those surveyed, do not want a new mall. how many people did annette survey? people

Explanation:

Step1: Find the percentage of people who want a new mall

If \(37.5\%\) do not want a new mall, then the percentage of people who want a new mall is \(100\% - 37.5\%=62.5\%=\frac{62.5}{100}=\frac{5}{8}\)

Step2: Set up an equation

Let the total number of people surveyed be \(x\). We know that the number of people who want a new mall is \(180\), and the proportion of people who want a new mall is \(\frac{5}{8}\). So we have the equation \(\frac{5}{8}x = 180\)

Step3: Solve for \(x\)

Multiply both sides of the equation \(\frac{5}{8}x=180\) by \(\frac{8}{5}\). Then \(x = 180\times\frac{8}{5}\)
\(x=\frac{180\times8}{5}= 288\)

Answer:

\(288\)